Chapter 3.14, Problem 13P

For each of the following sets, either verify (as in Example 1) that it is a vector space, or show which requirements are not satisfied. If it is a vector space, find a basis and the dimension of the space.

Verify $\left(14.7\right)$ and $\left(14.8\right)$ Hints: Remember that a norm squared, like is a real and non-negative.scalar, so its complex conjugate is just itself. But is a complex scalar and by $\left(14.4\right).$ Show that